Analysis: Use of asymmetrical pitch teeth to eliminate chatter

Chatter is a costly and persistent problem in milling. The effect of chatter vibration can be large enough to damage the tool, cause the workpiece to be scrapped, and even damage the machine tool. To make matters worse, due to the risk of chattering, machine tool operators may be too conservative in selecting processing parameters, making the machine's capabilities unable to make the best use of it. Usually, the processing capacity of the machine tool is only used one-half or a fraction of it.

Flutter is a kind of self-excited vibration, which means that the stable input energy from the spindle motor is converted into vibration through a certain mechanism. The main mechanism of machine tool vibration is the positive feedback amplification of vibration wave. Essentially, the dynamic rigidity of the machining system (including the tool and the workpiece) is insufficient. When the cutter tooth cuts the workpiece, it will cause vibration, and the vibrating cutter tooth will form ripples on the surface of the workpiece. When the next tooth is in contact with the corrugated surface, the surface corrugation will cause the chip thickness to change, the changed chip thickness will cause the cutting force to change, and the changed cutting force will cause vibration.

One way to eliminate the chatter mechanism is to test the dynamic characteristics of the machining system, use these test results to calculate a stable cutting area map, and select the cutting conditions within the stable range. This pre-control range strategy relies on adjusting the tool vibration to coincide with the corrugated surface. When the front and back corrugations coincide with each other, the chip thickness no longer changes and the vibration stops. When the number of vibration waves between adjacent teeth is exactly 1, 2 or any integer, a stable interval appears on the stability sine curve graph. This kind of processing strategy needs to know the stable speed, maintain a stable speed within the allowable spindle speed range, have evenly distributed cutter teeth, and accurately control the spindle speed.

An alternative strategy is to suppress the positive feedback amplification mechanism of vibration waves by changing the tooth spacing. If the cutter teeth have an asymmetric (uneven) pitch, the corrugated surface left by the previous cutter tooth cut by each cutter tooth has a different wave shape, thereby suppressing vibration. Compared with tools with equally spaced teeth, tools with unequal tooth spacing can generally achieve a more stable axial cutting depth.

However, to obtain such results, careful estimation is required. Because the feed is constant, the change of the tooth pitch will cause the feed per tooth to be different. This usually means that only one tooth can withstand the full chip load, while the rest of the teeth cannot cut at full load. For this reason, the effective feed per revolution of the tool must be reduced, and the reduction in feed must be matched by increasing the axial depth of cut until the teeth are just balanced.

For example, let us consider a 4-flute end mill with uniformly distributed teeth and the most stable axial depth of cut (10mm). The teeth are uniformly distributed at 90°, and the arrangement directions are 0°, 90°, 180° and 270° respectively. If the allowable chip load (feed per tooth) is 0.2mm, the feed per revolution will be 0.8mm/rev. If the orientation of only one tooth changes by 10°, the orientation of these teeth will be 0°, 100°, 190°, and 280°. Therefore, the tooth spacing is 100° (maximum spacing), 90°, 90° and 80° (minimum spacing).

In order to keep the feed per tooth at the maximum spacing from exceeding the allowable limit value, the maximum spacing is used as the control spacing. It is necessary to reduce the feed amount in accordance with the ratio of the equal spacing to the maximum spacing (90°/100° in this example) on the basis of the equally spaced cutter tooth feed. In this way, the chip loads corresponding to each interval between the teeth are 0.2mm, 0.18mm, 0.18mm and 0.16mm, respectively. The feed per revolution is 0.72mm/rev. For this tool, the allowable increase in the stable axial depth of cut must be greater than the 100/90 ratio, which means that 11.1mm is just the critical value of the metal removal rate. Generally speaking, when using this method to suppress the positive feedback amplification of vibration wave, in order to make the unequal spacing tool have application value, it is necessary to allow the axial depth of cut to double the ratio of maximum spacing/equal spacing.

Similarly, changing the spindle speed can also suppress the positive feedback amplification of the vibration wave, but when the spindle rotates more than one revolution, the tool tooth spacing can also be effectively changed. However, since the feed is fixed, the maximum distance can still control the feed. Before any increase in the metal removal rate can be achieved, the change in spindle speed must allow the stable axial depth of cut to double the maximum pitch/equal pitch ratio.